Quantum Cryptography

Lecture spring 2023

Instructor Dominique Unruh
TA Raul-Martin Rebane (submit homework solutions here)
Lecture Period February 6 - May 23
Lectures Mondays, 12:15-13:45, Δ-1022 (Dominique; may sometimes be switched with tutorial)
Practice sessions
Tuesdays, 10:15-12:00, Δ-2045 (Raul-Martin)
Course Material Lecture notes, recordings, blackboard photos, and exam study guide.
Language English
Exam 2023-05-25, 10:00–13:00, Delta room 1008
Contact Dominique Unruh <<surname>at ut dot ee>

Topics covered

DateSummaryKnowlets coveredMaterials
Feb 06General intro. Quantum systems, quantum statesQStateVideo, Whiteboard
Feb 07Unitary operations, measurements in computational basis, Elitzur-Vaidman bomb testerUniTrafo, CBMeas, PauliX, PauliY, PauliZ, BombVideo, Whiteboard
Feb 13Complete measurements. Projective measurements (subspace view).ComplMeas, ProjMeasVS, HadaVideo, Whiteboard
Feb 14Quantum Zeno effect, polarization invariant under rotation.ComplMeas, ConjTrans, DiracWhiteboard
Feb 20Projective measurements (projector view). Tensor product. Composition of quantum systems / quantum states / unitaries / measurements.ProjMeas, ComposQSys, ComposQState, Tensor, ComposUni, ComposMeasVideo, Whiteboard
Feb 21Using tensor product and proj. measurements. Quantum teleportationProjMeas, Tensor, ComposUni, ComposMeas, CNOT, HadaWhiteboard
Feb 27Quantum state probability distributions (ensembles). Operations on quantum state probability distributions. Density operators. Operations on density operators. Theorem: Physically indistinsuishable iff same density operator.QDistr, PhysInd, QDistrU, QDistrX, QDistrM, Density, Density, DensityU, DensityM, DensityX, DensityPhysIndVideo, Whiteboard
Feb 28Density operators. Implementing boolean unitariesQDistr, QDistrM, Density, DensityPhysInd, ToffWhiteboard
Mar 06Quantum One-Time Pad. Partial Trace.QOTP, ParTrVideo, Whiteboard
Mar 07Backwards toy crypto. Calculating Partial Trace. Tracing out buffer qubits in $U_f$. Impossibility of FTL communication.ParTrWhiteboard
Mar 13Motivation for trace distance. Statistical distance. Trace distance. Quantum operations.SD, SDSumDef, SDProps, TD, TDMaxDef, TDSD, TDProps, QOper, QOperAltVideo, Whiteboard
Mar 14Trace Distance of lecture example. QOTP with no zero-keys. Replace as Kraus operator. Trace Distance between arbitrary states.QOper, ParTr, SD, SDSumDefWhiteboard
Mar 20Quantum key distribution: Intro. Security definition. Protocol overview.QKDIntro, QKDSecDef, QKDProtoVideo, Whiteboard
Mar 21Prob. of measuring key after QKD. Alternate sec def of QKD. SMT from QKD.QKDSecDefWhiteboard
Mar 27Quantum key distribution: First step (distributing Bell pairs). Bell test. Measuring the raw key. Min-entropy.Bell, TildeNotation, BellTest, BellTestAna, RawKey, RawKeyKeyDiff, RawKeyGuess, MinEnt, RawKeyEnt, RawKeyAnaVideo, Whiteboard


Your current amount of points in the homework can be accessed here (as soon as the first sheet has been corrected).
Out Due Homework Solution
2023-02-132023-02-20Homework 1Solution 1
2023-02-202023-02-27Homework 2Solution 2
2023-02-272023-03-06Homework 3Solution 3
2023-03-062023-03-13Homework 4Solution 4
2023-03-132023-03-20Homework 5Solution 5
2023-03-202023-03-27Homework 6 
2023-03-272023-04-03Homework 7 


In quantum cryptography we use quantum mechanical effects to construct secure protocols. The paradoxical nature of quantum mechanics allows for constructions that solve problems known to be impossible without quantum mechanics. This lecture gives an introduction into this fascinating area.

Possible topics include:


You need no prior knowledge of quantum mechanics. You should have heard some introductory lecture on cryptography. You should enjoy math and have a sound understanding of linear algebra.


[NC00] Nielsen, Chuang. "Quantum Computation and Quantum Information" Cambridge University Press, 2000. A standard textbook on quantum information and quantum computing. Also contains some quantum cryptography.

Further reading may be suggested during the course. See the "further reading" paragraphs in the lecture notes.